A ball is dropped from a height metres and rebounds vertically each time to a…
MATHEMATICS · Multi-part · A Level · Mathematics · Sequences and series · Sequences and series
Problem
A ball is dropped from a height h metres and rebounds vertically each time to a fraction r (0<r<1) of the height from which it fell.
(i) Derive an expression, in terms of h, r and n, for the total vertical distance travelled by the ball up to and including the (n+1)th impact with the ground (that is, after n complete rebounds).
(ii) Using the expression from part (i), calculate the total distance covered when h=2m, r=0.6 and n=5. Round your answer to two decimal places.
(iii) If the ball continues to rebound indefinitely, determine the limiting value of the total distance travelled and state the condition under which this limit exists.